One-dimensional mixed MHD convection

The parallel, fully developed flow of an electrically conducting fluid between plane parallel walls under the simultaneous influence of a driving pressure head, buoyancy, and magnetohydrodynamic (MHD) forces is studied. The fluid is assumed to be internally heated and the flow is modeled as one-dimensional and incompressible, while the Boussinesq approximation is adopted for the buoyancy terms. Analytical solutions are obtained for temperature, velocity and electrical potential under different electrical boundary conditions, forced to natural convection intensity ratios and values of the magnetic induction. Generalized working charts are presented which synthetically describe the system’s operation as an EM pump, a MHD generator, a thermal engine or a pure dissipator.